Inverse Problems for Heat Convection System for Incompressible Viscoelastic Fluids

IF 0.8 Q2 MATHEMATICS Lobachevskii Journal of Mathematics Pub Date : 2024-08-22 DOI:10.1134/s1995080224601152
S. N. Antontsev, Kh. Khompysh
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Abstract

The paper deals the study some inverse source problems for heat convection system which consists of Kelvin–Voigt equations governing an incompressible viscoelastic non-Newtonian flows and a heat equation. The studying inverse problems consist of recovering a time depended intensity \(f(t)\) of a density of external forces and an intensity \(j(t)\) of a heat source, in addition to a velocity \(\mathbf{v}\), a pressure \(\pi\), and a temperature \(\theta\). As an additional information two types of integral overdetermination conditions over the domain are considered. For nonlinear inverse problem, under suitable conditions on the data, the local in time existence and uniqueness of weak and strong solutions are established. Some special cases of original inverse problem also investigated which allow global unique solvability.

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不可压缩粘弹性流体热对流系统的逆问题
摘要 本文涉及热对流系统的一些逆源问题研究,该系统由控制不可压缩粘弹性非牛顿流的开尔文-沃依格方程和热方程组成。研究的逆问题包括恢复外力密度的随时间变化的强度(f(t))和热源的强度(j(t)),此外还有速度(mathbf{v})、压力(pi)和温度(theta)。作为附加信息,还考虑了域上的两种积分超定条件。对于非线性逆问题,在数据的适当条件下,建立了弱解和强解在时间上的局部存在性和唯一性。此外,还研究了原始逆问题的一些特例,这些特例允许全局唯一可解性。
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来源期刊
CiteScore
1.50
自引率
42.90%
发文量
127
期刊介绍: Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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